hw15 - U = max X,Y Problem 15B X and Y are positive random...

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ENEE 324 ASSIGNMENT 15 Due Tue 11/03 Problem 15A X and Y are independent and identically distributed random variables with pdf f X ( t ) = f Y ( t ) = ( 1 / ( t + 1) 2 , t 0; 0 , t < 0. (i) (2 pts.) Sketch the region on the ( x,y ) plane where the random pair ( X,Y ) takes values. Give a formula for the joint pdf f XY ( x,y ) for every point on the ( x,y ) plane. (ii) (4 pts.) Explain (without computation) why P [ X > Y ] = 1 / 2. (iii) (7 pts.) Evaluate P [ X > 2 Y ]. ( A partial fraction expansion will be needed. ) (iv) (3 pts.) For u 0, determine P [ X u,Y u ] in terms of u . (v) (4 pts.) Based on your answer to part (iv), obtain the cdf and pdf of the random variable
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Unformatted text preview: U = max { X,Y } . Problem 15B X and Y are positive random variables such that f XY ( x,y ) = ( cx 2 (1-y ) , ≤ x ≤ y ≤ 1; , otherwise. The constant c is to be determined. (i) (2 pts.) Sketch the region on the ( x,y ) plane where the random pair ( X,Y ) takes values. (ii) (5 pts.) Determine the pdf of X in terms of c . (iii) (5 pts.) Repeat for the pdf of Y . (iv) (3 pts.) Using the result of (ii) or (iii) above, evaluate c . (v) (5 pts.) Evaluate P [ X + Y ≤ 1]....
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